Purpose -Power-electronic systems have been playing a significant role in the integration of large-scale wind turbines into power systems due to the fact that during the past three decades power-electronic technology has experienced a dramatic evolution. This second part of the paper aims to focus on a comprehensive survey of power converters and their associated control systems for high-power wind energy generation applications. Design/methodology/approach -Advanced control strategies, i.e. field-oriented vector control and direct power control, are initially reviewed for wind-turbine driven doubly fed induction generator (DFIG) systems. Various topologies of power converters, comprising back-to-back (BTB) connected two-and multi-level voltage source converters (VSCs), BTB current source converters (CSCs) and matrix converters, are identified for high-power wind-turbine driven PMSG systems, with their respective features and challenges outlined. Finally, several control issues, viz., basic control targets, active damping control and sensorless control schemes, are elaborated for the machine-and grid-side converters of PMSG wind generation systems. Findings -For high-power PMSG-based wind turbines ranging from 3 MW to 5 MW, parallel-connected 2-level LV BTB VSCs are the most cost-effective converter topology with mature commercial products, particularly for dual 3-phase stator-winding PMSG generation systems. For higher-capacity wind-turbine driven PMSGs rated from 5 MW to 10 MW, medium voltage multi-level converters, such as 5-level regenerative CHB, 3-and 4-level FC BTB VSC, and 3-level BTB VSC, are preferred. Among them, 3-level BTB NPC topology is the favorite with well-proven technology and industrial applications, which can also be extensively applicable with open-end winding and dual stator-winding PMSGs so as to create even higher voltage/power wind generation systems. Sensorless control algorithms based on fundamental voltages/currents are suggested to be employed in the basic VC/DPC schemes for enhancing the robustness in the entire PMSG-based wind power generation system, due to that the problems related with electromagnetic interferences in the position signals and the failures in the mechanical encoders can be avoided. Originality/value -This second part of the paper for the first time systematically reviews the latest state of arts with regard to power converters and their associated advanced control strategies for high-power wind energy generation applications. It summarizes a variety of converter topologies with pros and cons highlighted for different power ratings of wind turbines.